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3 years ago

I need help with this

Mathematics

1 answer:

yanalaym [24]3 years ago

3 0

Answer:

104

Step-by-step explanation:

8x3=24 then you carry over the 2 and 8x1=8 and 8+2=10 so the awnser is 104

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Find the inverse Laplace transforms, as a function of x, of the following functions:

inn [45]

Answer: The required answer is

$f(x)=e^x+\cos x+\sin x.$

Step-by-step explanation: We are given to find the inverse Laplace transform of the following function as a function of x :

$F(s)=\dfrac{2s^2}{(s-1)(s^2+1)}.$

We will be using the following formulas of inverse Laplace transform :

$(i)~L^{-1}\{\dfrac{1}{s-a}\}=e^{ax},\\\\\\(ii)~L^{-1}\{\dfrac{s}{s^2+a^2}\}=\cos ax,\\\\\\(iii)~L^{-1}\{\dfrac{1}{s^2+a^2}\}=\dfrac{1}{a}\sin ax.$

By partial fractions, we have

$\dfrac{s^2}{(s-1)(s^2+1)}=\dfrac{A}{s-1}+\dfrac{Bs+C}{s^2+1},$

where A, B and C are constants.

Multiplying both sides of the above equation by the denominator of the left hand side, we get

$2s^2=A(s^2+1)+(Bs+C)(s-1).$

If s = 1, we get

$2\times 1=A(1+1)\\\\\Rightarrow A=1.$

Also,

$2s^2=A(s^2+1)+(Bs^2-Bs+Cs-C)\\\\\Rightarrow 2s^2=(A+B)s^2+(-B+C)s+(A-C).$

Comparing the coefficients of x² and 1, we get

$A+B=2\\\\\Rightarrow B=2-1=1,\\\\\\A-C=0\\\\\Rightarrow C=A=1.$

So, we can write

$\dfrac{2s^2}{(s-1)(s^2+1)}=\dfrac{1}{s-1}+\dfrac{s+1}{s^2+1}\\\\\\\Rightarrow \dfrac{2s^2}{(s-1)(s^2+1)}=\dfrac{1}{s-1}+\dfrac{s}{s^2+1}+\dfrac{1}{s^2+1}.$

Taking inverse Laplace transform on both sides of the above, we get

$L^{-1}\{\dfrac{2s^2}{(s-1)(s^2+1)}\}=L^{-1}\{\dfrac{1}{s-1}\}+L^{-1}\{\dfrac{s}{s^2+1}+\dfrac{1}{s^2+1}\}\\\\\\\Rightarrow f(x)=e^{1\times x}+\cos (1\times x)+\dfrac{1}{1}\sin(1\times x)\\\\\\\Rightarrow f(x)=e^x+\cos x+\sin x.$

Thus, the required answer is

$f(x)=e^x+\cos x+\sin x.$

4 0

4 years ago

What would be the equation for #23???

Rufina [12.5K]

Hi there!

Let r be the number of matches that Rebecca's team won.

We know that Katheryn's team won 9 more matches than Rebecca's team, and we know that Katheryn's team won 52 matches.

Using this given information, we can create the following equation.

$r+9=52$

If you wish to solve this, we can subtract both sides by 9 to get the following value for r.

$r=43$

Have an awesome day! :)

~collinjun0827, Junior Moderator

8 0

3 years ago

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What is an equation of the line that passes through the points (4,-6) and has a slope of -3

lions [1.4K]

Answer:

Step-by-step explanation:

point slope form

y + 6 = -3(x - 4)

point slope to y-intercept

y + 6 = -3x + 12

y = -3x + 6

3 0

3 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Aleksandr [31]

Answer:

Step-by-step explanation:

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3 years ago

Whats is the cost of electricity to run personal computer

Brrunno [24]

Answer: Desktop computers can cost anywhere from $300-$4,000 depending on how good it's inside components are. The average computer might go for around $400. For more advanced computers the price might be $1,000 or more. All in all, the cost of a computer / PC truly depends on how much power you're needing from it.

Step-by-step explanation:

Srry its kinda confusing but I hope it helped

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3 years ago

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